Spectrum of magnetohydrodynamic turbulence

Abstract

We propose a phenomenological theory of strong incompressible magnetohydrodynamic turbulence in the presence of a strong large-scale external magnetic field. We argue that in the inertial range of scales, magnetic-field and velocity-field fluctuations tend to align the directions of their polarizations. However, the perfect alignment cannot be reached, it is precluded by the presence of a constant energy flux over scales. As a consequence, the directions of fluid and magnetic-field fluctuations at each scale $λ$ become effectively aligned within the angle $ϕ_λ\propto λ^{1/4}$, which leads to scale-dependent depletion of nonlinear interaction and to the field-perpendicular energy spectrum $E(k_{\perp})\propto k_{\perp}^{-3/2}$. Our results may be universal, i.e., independent of the external magnetic field, since small-scale fluctuations locally experience a strong field produced by large-scale eddies.